This proposal is for mathematical modeling of three features of renal function: (1) the dynamics of tubuloglomerular feedback; (2) the dynamics of the renal papilla; and (3) the structural and functional heterogeneity of the renal medulla. This research will elucidate (1) the origin, character, and long-time behavior of oscillations in pressure, fluid flow, and solute concentrations in the in the tubules of nephrons; (2) the role of papillary peristalsis in intratubular fluid connection, in transtubular water and solute transport, and in the generation and maintenance of the inner medullary concentration gradient; and (3) the importance of distributed loops of Henle, of variation in single nephron glomerular filtration rates as a generation of the medullary concentration gradient. The principal mathematical methods that will be employed in each of the three projects are (1) flux-corrected transport for the solution of systems of hyperbolic partial differential equations; (2) the technique of Charles S. Peskin and David M. McQueen for the solution of the Navier-Stokes equations in a region containing an immersed boundary; and (3) fixed-point iteration and continuation of parameters for the solution of systems of integro-differential equations. The models will be developed in consultation/collaboration with numerical analysts and physiologists. Every effort will be made to ensure the mathematical integrity and physiological applicability of the results. Because many issues in renal physiology remain unresolved and because much new experimental data needing interpretation is being generated, the integrative work proposed here may contribute significantly to the understanding of normal renal function. Such understanding is essential, over the long term, for progress in the analysis and treatment of kidney disease.